We introduce and generate the partially coherent non{canonical vortex beams and study their characteristics. The characterization of these fields by means of its intensity is difficult due to the random fluctuations in space and time of partially coherent fields, but it is demonstrated that the cross{correlation function provides information of the composition, spatial coherence structure and singularities of the non{canonical vortex beams. Our approach is based on experimental measurements and numerical simulations of these beams, which show excellent agreement.
The intensity distributions of self-focusing dual Airy beams are studied analytically by means of their statistical moments. Closed form expressions are derived that allow the determination of the focal shift through two different criteria; the first one is based on the second moment of the intensity whereas the second takes advantage of the beams symmetry to employ encircled-power calculations for defining the focus. Our results confirm the existence of a focal shift as expected, and show an effective quadratic dependence on the truncation parameter of the Airy beams.
We study both theoretically and experimentally the cross-correlation function of single-ringed Laguerre-Gaussian (LG) beams, which allows us to determinate the topological charge of the beam by performing power measure-ments only. We employ a superposition of two exact copies of the original LG beam whose centroids are displaced from each other. The behaviour of the auto-correlation is studied as a function of the displacement between these two copies of the beam for different topological charges. Our results indicate that the auto-correlation is described by a polynomial function of the displacement parameter, and the number of zeros of this polynomial maintains a one to one correspondence with the topological charge. A detailed description of the experiment to perform these measurements is also provided, our experimental findings are in excellent agreement with the theory. This technique offers an alternative for measuring the content of orbital angular momentum in a beam without the need of a camera.
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